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Observational ultraproducts of polynomial coalgebras

2003
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Annals of Pure and Applied Logic
*

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Ultraproducts of Tannakian Categories and Generic Representation Theory of Unipotent Algebraic Groups
[article]

2010
*
arXiv
*
pre-print

,

arXiv:1011.0460v1
fatcat:egfuzgtem5ewbfhx3dldm2elsi
*ultraproducts**of*them. ... One*of*the main theorems*of*this dissertation is that certain naturally definable subcategories*of*these*ultraproducts*are themselves neutral tannakian categories, hence tensorially equivalent to Comod_A ... The representing Hopf algebra*of*the restricted*ultraproduct*R Comod A i is*coalgebra*-isomorphic to the restricted*ultraproduct*A R*of*the Hopf algebras A i .Proof. ...##
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6 Algebras and coalgebras
[chapter]

2007
*
Studies in Logic and Practical Reasoning
*

In the second and last part

doi:10.1016/s1570-2464(07)80009-7
fatcat:e77uebqxdferlcg2nlfe5hobpq
*of*the chapter we describe how modal logic, and its model theory, provides many natural manifestations*of*the more general theory*of*universal*coalgebra*. 1 This text has been ... This chapter 1 sketches some*of*the mathematical surroundings*of*modal logic. ... Acknowledgments Many people have contributed to this chapter by commenting on earlier versions*of*it. ...##
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A comonadic account of behavioural covarieties of coalgebras

2005
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Mathematical Structures in Computer Science
*

K may be thought

doi:10.1017/s096012950400458x
fatcat:g5aflvvy4rbkhoa45l7d3dnina
*of*as the class*of*all*coalgebras*that satisfy some computationally significant property. ... We show that there is a bijective correspondence between behavioural covarieties*of*T -*coalgebras*and isomorphism classes*of*pure subcomonads*of*G T . ...*of**observational*ultrapowers*of**polynomial**coalgebras*in (Goldblatt, 2003c) . ...##
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Probabilistic logics based on Riesz spaces

2019
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Logical Methods in Computer Science
*

By using powerful results from this theory, we develop the duality theory

doi:10.23638/lmcs-16(1:6)2020
fatcat:vqm3un3yqfbs3nckws4dnqqzpu
*of*the Riesz modal logic in the form*of*an algebra-to-*coalgebra*correspondence. ... The design*of*the syntax and semantics*of*this logic is directly inspired by the theory*of*Riesz spaces, a mature field*of*mathematics at the intersection*of*universal algebra and functional analysis. ... Acknowledgements The work*of*Mio has been partially supported by the French project ANR-16-CE25-0011 REPAS. ...##
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Probabilistic logics based on Riesz spaces
[article]

2020
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arXiv
*
pre-print

By using powerful results from this theory, we develop the duality theory

arXiv:1903.09463v3
fatcat:pqk4bz4hiffxbklkm33ovkrehe
*of*the Riesz modal logic in the form*of*an algebra-to-*coalgebra*correspondence. ... The design*of*the syntax and semantics*of*this logic is directly inspired by the theory*of*Riesz spaces, a mature field*of*mathematics at the intersection*of*universal algebra and functional analysis. ... Acknowledgements The work*of*Mio has been partially supported by the French project ANR-16-CE25-0011 REPAS. ...##
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Cocommutative coalgebras: homotopy theory and Koszul duality

2016
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Homology, Homotopy and Applications
*

We extend a construction

doi:10.4310/hha.2016.v18.n2.a17
fatcat:p5kkrcak2vaorppexqryf5kigm
*of*Hinich to obtain a closed model category structure on all differential graded cocommutative*coalgebras*over an algebraically closed field*of*characteristic zero. ... We further show that the Koszul duality between commutative and Lie algebras extends to a Quillen equivalence between cocommutative*coalgebras*and formal coproducts*of*curved Lie algebras. ... dg*coalgebras*over a field*of*characteristic zero. ...##
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Cocommutative coalgebras: homotopy theory and Koszul duality
[article]

2014
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arXiv
*
pre-print

We extend a construction

arXiv:1403.0774v1
fatcat:bhxlr4xnk5grdd3qcqmz6aqizm
*of*Hinich to obtain a closed model category structure on all differential graded cocommutative*coalgebras*over an algebraically closed field*of*characteristic zero. ... We further show that the Koszul duality between commutative and Lie algebras extends to a Quillen equivalence between cocommutative*coalgebras*and formal coproducts*of*curved Lie algebras. ... dg*coalgebras*over a field*of*characteristic zero. ...##
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Metamathematics for Systems Design

2017
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New generation computing
*

However, there are fundamental gaps in application

doi:10.1007/s00354-017-0023-1
fatcat:pw6byl77njf2boltl4qbjdh3ba
*of*formal methods to industry products: additional concerns in industry products such as continuous dynamics*of*physical components and quantitative measures ... This position paper describes the context, the goal, the strategy and the tactics*of*the ERATO MMSD project (2016-2022. ... Acknowledgements Thanks are due to the following people: the core members*of*the ERATO MMSD project (Krzysztof Czarnecki, Masahito Hasegawa, Fuyuki Ishikawa, Shin-ya Katsumata, Kohei Suenaga, Toshimitsu ...##
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Page 852 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

(Natalia Bebiano) 2004d:15010 15A15 (15A48)
Goldblatt, Robert

*Observational**ultraproducts**of**polynomial**coalgebras*. (English summary) Ann. Pure Appl. Logic 123 (2003), no. 1-3, 235-290. ... The Sylvester resultant matrix for Bernstein*polynomials*. (English summary) Curve and surface design (Saint-Malo, 2002), 407-416, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2003. ...##
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Fourier's Method of Linear Programming and Its Dual

1986
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The American mathematical monthly
*

systems, model-matching, etc.)
93A99
None

doi:10.2307/2322281
fatcat:yvhgyh2epbcwdoqdhuaopkcrue
*of*the above, but in this section 93Bxx Controllability,*observability*, and system structure 93B03 Attainable sets 93B05 Controllability 93B07*Observability*...*of*functions 26B99 None*of*the above, but in this section 26Cxx*Polynomials*, rational functions 26C05*Polynomials*: analytic properties, etc. ...*Observational*and experimental questions 83B05*Observational*and experimental questions 83B99 None*of*the above, but in this section 83Cxx General relativity 83C05 Einstein's equations (general structure ...##
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On the Frobenius functor for symmetric tensor categories in positive characteristic
[article]

2020
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arXiv
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pre-print

We develop a theory

arXiv:1912.12947v2
fatcat:d5ztonbzg5ap3k6ovfxenrsnvm
*of*Frobenius functors for symmetric tensor categories (STC) C over a field k*of*characteristic p, and give its applications to classification*of*such categories. ... We also show that a sufficiently large power*of*F lands in C_ ex. ... The work*of*P. E. was partially supported by the NSF grant DMS-1502244. The work*of*V. ...##
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Definable additive categories: purity and model theory

2011
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Memoirs of the American Mathematical Society
*

In particular, if F commutes with

doi:10.1090/s0065-9266-2010-00593-3
fatcat:a5cgsl5w5bgpfidsdqb4jcw5qi
*ultraproducts*(meaning, commutes with those*ultraproducts**of*pureinjective objects*of*D which are themselves pure-injective) then (F p /F ψ ) D must be a finitely generated ... We consider a functor from Mod-k[T ] to Mod-k A 1 , where k is a field, k[T ] is the*polynomial*ring and k A 1 is the path algebra*of*the Kronecker quiver A 1 . ...##
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Complete Additivity and Modal Incompleteness
[article]

2018
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arXiv
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pre-print

On the other hand, we

arXiv:1809.07542v1
fatcat:priuo4blnjhozdoajxxfyy6f6y
*observe*that it is undecidable whether a syntactically defined logic is V-complete. After these results, we generalize the Blok Dichotomy to degrees*of*V-incompleteness. ... In the end, we return to van Benthem's theme*of*syntactic aspects*of*modal incompleteness. ... This by itself does not lead to "natural" examples*of**coalgebraic*logics where mild rules like our V-mod are inadmissible;*coalgebraic*logicians focus almost exclusively on minimal logics, axiomatizable ...##
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Extending torsors on the punctured Spec(A_inf)
[article]

2020
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arXiv
*
pre-print

As applications we extend results

arXiv:1804.06356v2
fatcat:m7ydzra565fybc4rg57oxezbiy
*of*Ivanov on exactness*of*the loop functor and present the construction*of*a canonical specialization map from the B^+_dR-affine Grassmannian to the Witt vector affine ... Using descent we can extend a similar result for the ring 𝔖*of*Kisin and Pappas to full generality. Moreover, we treat similarly the case*of*equal characteristic. ... This equivalence respects tensor products and hence induces an equivalence on algebra/*coalgebra*objects. ...
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